
theorem
  for L being domRing
  for p being non-zero Polynomial of L st Roots p = {} holds
  SumRoots p = 0.L
  proof
    let L be domRing;
    let p be non-zero Polynomial of L such that
A1: Roots p = {};
    canFS Roots p is Enumeration of Roots p by Th2;
    then BRoots(p)(++)canFS Roots p = {} by A1,Th18;
    then len (BRoots(p)(++)canFS Roots p) = 0;
    hence thesis by RLVECT_1:75;
  end;
